In Room 307 of Manhattan’s Stuyvesant High School, 23 students spent a recent afternoon copying tables and number trees representing a mathematical problem-solving technique used in graphic design computer software.

The students, who all won admission to Stuyvesant by posting top scores on an entrance exam, listened raptly as their teacher, Mike Zamansky, walked them through the complex algorithm behind “seam-carving,” a process used in resizing images. Then Zamansky checked to make sure they understood.

“No problem? Seems reasonable? or ‘Huh’?” he asked, offering students the chance to signal by a show of thumbs whether they understood or needed more help. No one pointed a thumb down.

Zamansky has been teaching computer science since 1995, through a program he designed for students to follow from sophomore to senior year. Stuyvesant’s program is the only rigorous computer science sequence in the city’s public schools and one of the few in the country.

Now it is the inspiration behind a new city high school that aims to change that.

Founded by an influential venture capitalist with deep ties to the technology industry and a young principal fresh from the city’s training program, the Academy for Software Engineering will be the city’s first school to focus on software engineering. The goal is to extend the approach of Zamansky’s classes — which teach problem-solving, network communications, and programming language literacy — to any student in the city, even if they can’t make the cut for Stuyvesant or don’t even have a computer at home.

Mayor Bloomberg championed the school in his January State of the City Address, and the Panel for Educational Policy last month signed off plans for it to open inside Union Square’s Washington Irving High School, which is set to close because of poor performance.

AFSE will admit students through a “limited unscreened” process, meaning that any student in the city can apply, and the only criterion the school can use to rank them is whether they showed interest by attending a high school fair or information session. The open-door policy means some students who enroll could live in homes without computers or an internet connection.

Making computer science available to anyone who is interested been part of the plan since the school’s earliest days as a figment of Fred Wilson’s imagination.

Wilson, one of AFSE’s founders and its prime fundraiser, reached out to Zamansky in 2008 after readers of Wilson’s popular venture capitalism blog who had graduated from Stuyvesant praised the teacher for setting them up for careers in software engineering. Wilson had no background in education but wanted to learn more about how the program worked and whether it could be replicated outside of the city’s most selective high schools.

“One of the questions I asked him was, why isn’t more of this happening across the school system?” Wilson said. “There’s fear that this stuff is really, really hard and that you need to be like an elite student to take it.”

Zamansky was intrigued but skeptical that a diverse group of 14-year-olds, including those from low-income or non-English speaking backgrounds, could be taught in four years how to create computer software at a level that would make them employable in the city’s burgeoning technology sector.

“If the goal is to make Google-quality engineers, I graduate Google-quality engineers. And starting with raw material that is ahead of grade level has a lot to do with it,” Zamansky said. “But a group of programmers who are gainfully employed? That’s a much more realistic goal.”

Wilson said he would hear that skepticism echoed in the conversations that followed with donors, educators, and Department of Education officials. But he said AFSE would upend the notion that only top students can learn challenging subjects.

“They’re in effect creating quasi-private schools, and that’s not nearly as ambitious as what we’re trying to do,” Wilson said about the city’s specialized high schools. “Rightly, a lot of principals feel like, ‘I can’t just take the Stuy curriculum and dump that on my kids.’ But we can show people how to do it. If we can do this, we will have a curriculum that can be rolled out citywide.”

Wilson said he also got raised eyebrows when he first approached city officials with the idea for the school three years ago. But he got the chance to convince them last year, when he met with Josh Thomases and Gregg Betheil, top Department of Education deputies, just as the city was beginning to focus on aligning career and technical education programs with expanding job markets. They said he had the department’s support but would need to raise funds to pay for a principal, program manager, and teacher training sessions well in advance of the school’s opening, according to Wilson. He would also need to form an advisory board to develop the curriculum, he said.

Wilson said the school’s startup costs have been steeper than for most schools because of its unusual focus. He would not share the amount of funding the school required but said he had met the fundraising goals with the help of an advisory board of fellow industry leaders, including employees of Google, Facebook and eBay; computer science educators; and a newly hired principal, Seung Yu.

Yu, selected last month to be the school’s founding principal, said he is excited about the prospect of introducing computer science and software engineering lessons to students from a range of skill levels — but he knows the challenge will be steep. A participant in the city’s Leadership Academy Aspiring Principals Program, Yu is being mentored by Rashid Davis, who runs Pathways to Technology Early College High School, a technology-focused high school that opened in 2011.

“I do recognize there will be quite a few students who come in with low level skills,” Yu said. “This is why we’re a small school. There’s beauty in that, being limited unscreened. We will have to look at what those students need in order to be successful.”

The school aims to enroll about 108 new students each year and ultimately max out with an enrollment of 432.

Zamansky, who has participated in the advisory board’s meetings, told me he supports their goals but remains wary of the small school model. He argued that students’ potentially widely varied abilities might call for more differentiated instruction than a small school could hope to offer.

“I think you can take any population and move it forward. But it will be very difficult to give meaningful instruction unless the size is sufficient,” he said.

Zamansky said he would like to see the DOE start by investing resources in expanded computer science offerings at other schools for gifted students, such as the Bronx High School of Science and Brooklyn Technical High School. If there were a critical mass of educators teaching high-level students, he said, teachers at settings like AFSE would have more colleagues to draw on for support.

But Zamansky also said he is frustrated by what he sees as a the lack of support to computer science instructors within the Department of Education and at Stuyvesant. One of the merits of starting fresh, he said, would be the ability to hire a staff committed to the computer sciences, which he cannot do as the unofficial program coordinator at his school.

AFSE’s structure and curriculum will largely mirror that of other recently opened small high schools, according to Yu. It will still offer English, history and other core courses, in addition to one or two computer science classes per year. The goal is for students to graduate able to study computer science in college, take entry-level software engineering jobs, or forgo software engineering entirely.

Exactly how computer science will be integrated into the traditional curriculum at AFSE is an open question that the advisory board plans to tackle in the coming months, according to Wilson and Yu. Science and math should be easy, Wilson said, but English and social studies could be less intuitive.

Because the school is beginning with just a ninth grade, it will need only one or two teachers with computer science backgrounds in the first year, Wilson and Yu said. Wilson said he is already receiving inquiries from public school teachers who are interested in computer science and software engineers working in the industry, who have seen the school’s vigorous promotions on technology blogs.

To drum up interest among students, Wilson and Seung have invited working software engineers to stand at their booth at a citywide fair for students who are still looking for a high school this weekend. Later this month, they will hold “open house” information sessions at the city headquarters of Google and New York University. Knowing software engineering could be a tougher sell for female students, Wilson said he is planning to ask female engineers to tout the school.

Wilson said the technology community’s eagerness to support AFSE reflects an awareness of the untapped potential of the city’s students, who he hopes will be set on a path to high-paying jobs at well-known tech companies.

“Software engineering is one of the — if not the — most in-demand job in the country right now,” Wilson said. “Every single one of these companies … they get frustrated that they can’t hire as fast as they want in New York City, so they start opening offices elsewhere. It would be really amazing if we could have our own kids growing up here become those software engineers.”